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arXiv · 2409.12465

Galileo: A Pseudospectral Collocation Framework for Legged Robots

Ethan Chandler·Akshay Jaitly·Mahdi Agheli
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Abstract

Dynamic maneuvers for legged robots present a difficult challenge due to the complex dynamics and contact constraints. This paper introduces a versatile trajectory optimization framework for continuous-time multi-phase problems. We introduce a new transcription scheme that enables pseudospectral collocation to optimize directly on Lie Groups, such as SE(3) and quaternions without special normalization constraints. The key insight is the change of variables - we choose to optimize over the history of the tangent vectors rather than the states themselves. Our approach uses a modified Legendre-Gauss-Radau (LGR) method to produce dynamic motions for various legged robots. We implement our approach as a Model Predictive Controller (MPC) and track the MPC output using a Quadratic Program (QP) based whole-body controller. Results on the Go1 Unitree and WPI HURON humanoid confirm the feasibility of the planned trajectories.

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Ethan Chandler, Akshay Jaitly, Mahdi Agheli. 2024-09-19. Galileo: A Pseudospectral Collocation Framework for Legged Robots. https://arxiv.org/abs/2409.12465

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